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The Quietest Challenge to the Axiology of God: A Cognitive Approach to Counterpossibles

Forthcoming in Faith and Philosophy

Joshua MuggIndiana University Kokomo

Abstract: Guy Kahane (2011, 2012) asks an axiological question: what value would (or does) God’s existence bestow on the world? Supposing God’s existence is a matter of necessity, this axiological question faces a problem because answering it will require assessing the truth-value of counterpossibles. I argue that Kahane, Moser, and Davis and Franks fail in their attempts to render the axiological question substantive. I then offer my own solution by bringing work in cognitive psychology and philosophy of mind to bear on the possibility of assessing counterpossibles. I argue that humans can engage in counterpossible reasoning by ‘accepting’ or ‘supposing’ that the antecedent is true and ‘screening out’ those beliefs that would result in contradictions when combined in inferences with the acceptance or supposition. These screened out propositions are not treated as false, but are ignored. I offer a three-valued logic for counterpossible reasoning. I then conclude by outlining some implications for the axiological question.

1. Introduction

Guy Kahane (2011, 2012) asks to what extent God’s existence would be (or is) valuable. Would God’s existence (or non-existence) increase or decrease the overall value of the world? This question concerning the value of God’s existence (call it the axiological question) must be sharply distinguished from the question of whether God exists. The axiological question is problematic, since answering it will require assessing the truth-value of what many philosophers take to be counterpossible conditionals. According to the theist who thinks God’s existence is necessary, the following conditional is a counterpossible: ‘if God did not exist, then the world would be better (or worse).’ Likewise, according to the atheist who thinks God’s nonexistence is necessary, the following is a counterpossible: ‘if God existed, then the world would be better (or worse).’ On standard semantics (such as both Lewis and Stalnaker’s), counterpossible conditionals are trivially true.1 Thus, the theist ought to judge that the world would be better if God were not to exist, but also that the world would be worse if God were not to exist. 2 Problematically, an axiological investigation of God’s existence cannot even get off the ground.

While philosophers writing on the axiological question are not ignorant of this problem (see Kraay & Dragos 2013, p. 160-161, Kahane 2011, p. 677, Kahane 2012, Mawson 2012, and Davis and Franks 2015), I argue that none of them offer a satisfying way of evaluating counterpossibles. I then offer a novel way of rendering the axiological question substantive. I

1 Standard possible world semantics says that a counterfactual is true just in case the consequent is true in the nearest possible world in which the antecedent is true. However, counterpossibles have antecedents that are false in all possible worlds (that is why they are counterpossibles); there is no closest possible world in which the antecedent is true. Thus, every counterpossible is trivially true because the antecedent is never fulfilled. Lewis (1973) says there is “at least some intuitive justification” for making counterpossibles trivially true, since we might respond to an impossibility: “if that were so, anything you like would be true!” (24, see 24-26 for a more detailed discussion).2 See Zagzebski (1990) for careful criticism of the standard semantics’ treatment of counterpossibles. Contra the standard semantics, Zagzebski argues that not all necessarily false propositions should be treated the same way; there are some ‘interesting impossible propositions’ (p. 174-175).

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suggest that humans should engage in counterpossible reasoning by ‘accepting’ or ‘supposing’ that the antecedent of the counterpossible conditional is true and ‘screening out’ those beliefs that would result in contradictions when combined with inferences from the acceptance or supposition. I suggest that the axiological investigation should use a three-valued logical system. The cognitive account of pretence I use offers a way to make sense of the third truth-value. When engaging in counterpossible reasoning, some propositions are ‘true,’ others ‘false,’ and still others ‘ignored.’ An implication of my approach to the axiological question is that some propositions should not be permitted in the dialectic between the pro and anti-theists.

2. Previous work on counterpossibles and the axiological question

Presumably responding to the axiological question requires comparing the overall value of states of affairs in which God exists (Godly states of affairs) and states of affairs in which God does not exist (Godless states of affairs). Doing so requires assessing the truth-value of the following four claims:

1. If God were to exist, the world would be better.2. If God were to exist, the world would be worse.3. If God were not to exist, the world would be better.4. If God were not to exist, the world would be worse.

Kraay and Dragos (2013) outline four positions one could take regarding the axiological question: pro-theism (1 or 4 are true, 2 or 3 are false), anti-theism (2 or 3 are true, 1 or 4 are false), indifferentism (1-4 are false), and agnosticism (unsure of the truth-value of 1-4).3 However, for anyone who thinks that God’s existence is a matter of necessity (i.e. God either exists necessarily or necessarily does not exist), either 1 and 2 are counterpossibles, or else 3 and 4 are. Thus, there is a fifth possible response to the axiological question: nothing at all can be said about the value of God’s existence or non-existence. I call this position ‘quietism.’ Quietism should not be confused with agnosticism on the axiological question. The quietist claims that the axiological question cannot be answered for metaphysical, rather than epistemic, reasons. According to the quietist, asking what value God would bestow on the world would be like asking what value a round square copula on Berkeley College would bestow upon the world. At best, the question is not substantive, at worst it is meaningless. The first task in answering the axiological question is to respond to the quietist’s objection.

One proposed solution is to distinguish 1-4 epistemically. Kahane (2012) initially considers this option, explaining that when we consider God’s necessary existence and necessary non-existence, at least one of these

does not describe a genuine possibility. They describe what are at most epistemic possibilities—ways in which things might turn out to be (even to necessarily be), for all we know. These epistemic possibilities will still be open to agnostics, or even to uncertain believers. But they will be closed to those who know that some position describes an impossibility—the possibility that God exists is closed to atheists who are certain that the concept of God is incoherent. (p. 35) 4

3 In principle, these four positions cross-cut theism, atheism, and agnosticism. Kraay and Dragos, with others, also distinguish between impersonal/personal and narrow/wide versions of each of these positions. These complications are not relevant to my present purposes. 4 We might add that these epistemic possibilities will be closed to those who believe they know that some position describes an impossibility. Genuine knowledge that theism or atheism is an impossibility is not required to awaken

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However, it is problematic that the ardent theist and atheist cannot even engage in the axiological question. It leads to the following:

If we knew that God necessarily exists, we could value His existence, and, in one sense, see it as making the world better. But we could no longer hold that it would be bad or worse if He didn’t exist. If this view is correct, then views and attitudes expressed by many theists (and, conversely, by many atheists) might not ultimately make sense. (p. 37)

I agree with Kahane that this epistemic solution is deeply flawed. Oddly, Kahane seems to allow that some views and attitudes might still make sense. Perhaps the theist can claim that God is good in a non-comparative way: God’s existence makes the world as good as it is.5 However, notice the kinds of claims the theist must give up if the theist tries to answer the axiological question in a non-comparative way. The theist would be unable to claim that God makes the world better than it would be if God did not exist. Likewise, claims that life would be meaningless without God would not make sense. Perhaps some will be willing to bite these bullets. But consider that non-comparative solutions to the axiological problem would be problematic for anyone who thinks that bringing pragmatic reasoning to bear on the existence of God makes sense. Bringing pragmatic reasons to bear on God’s existence involves comparing belief/non-belief in a godly state of affairs to belief/non-belief in a godless state of affairs. Even if one thought that we should not decide what to believe on pragmatic grounds (perhaps beliefs should only be altered for evidential reasons), it is surely odd to claim that Pascal-like considerations make no sense.

Kahane’s preferred solution is for each side to conceive of possibilities that are close to the impossibilities. For example,

Suppose…that the concept of an omnipotent, omniscient and perfectly good being was incoherent. The existence of an immensely knowledgeable, powerful and benevolent being might still be a genuine metaphysical possibility, and value claims about theism could migrate to this adjacent possibility, allowing us to make rational sense of the attitudes associated with these value claims. (2012, p. 38)

Moser (2013) makes a similar suggestion. Moser defines ‘God’ as a perfectionist title, which allows one to remain neutral about God’s existence for the purpose of the axiological question. Moser admits that exactly what content should be included with this title might be controversial. To echo Kahane, the very idea of an omnipotent, omnibenevolent, omniscient being might be incoherent. Moser’s solution is to start with the “highest perfectionist level…[and] lower the bar later if the former inquiry fails” (p. 273). So if the traditional theistic concept is incoherent, then we should conceive of a slightly less powerful, good, or knowledgeable being.

However, there is a problem with Kahane’s and Moser’s suggestion.6 Kahane’s necessitarian atheist is no longer thinking of a world with God in it, but rather a world with some super-human godlike being. It is plausible that by the time the atheist has weakened each property of God to their liking, it will be a god* unrecognizable. Maybe the addition of a really nice human, with lots of political, monetary, and societal power, and several advanced degrees

the quietist objection, since if S believes that they know that P is necessary, they will presumably claim that any conditional affirming not-P is a counterpossible.5 Thanks to Mark Murphy for this suggestion.6 I leave aside the problem of determining closeness of possibilities to impossibilities.

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would indeed make the world better, but this fact could hardly be taken to support pro-theism, since the term ‘God’ does not properly apply to this human.

Perhaps the solution lies in re-evaluating the standard semantics, as they do sometimes violate our intuitions. 7 Consider the following two claims from Morriston (2009):

5. If God were evil, he would be evil.6. If God were evil, he would be good.

Assuming that God (if such there be) is necessarily good, both are counterpossibles. While 5 is intuitively true, 6 is intuitively false. However, what grounds the difference in truth-value? Morriston (2012) explains that we can ground this difference in the fact that in 5, but not 6, “the antecedent does not entail the consequent merely in virtue of being impossible. It also does so because of the way in which its content is logically related to the consequent” (p. 20-21). Davis and Franks (2015) point out that Morriston is not thinking of entailment as ‘strict implication,’ since necessarily false propositions strictly imply every proposition. Instead, a counterpossible is true only if the content of the antecedent contains the content of the consequent. Otherwise it is false. However, Davis and Franks point out that Morriston’s method is too limited, since when we consider counterpossibles “we are asking what the extra-conceptual world would have been like had that antecedent been true” (p. 10).

Davis and Franks go on to argue that Morriston’s approach to counterpossibles suffers from a key problem. Namely, he does not consider the null world hypothesis—the claim that God’s existence is necessary for the world’s existence. On this view, if God had not existed, neither would anything else have existed. Given the null world hypothesis, counterpossibles are false when they fulfill two conditions: 1) the antecedent contains God’s non-existence and 2) the consequent implies the existence of at least one thing. While Davis and Franks use the null world hypothesis to argue that Morriston’s attack on divine command theory fails, their approach implies quietism about the axiological question. According to Davis and Franks, both of the following are false:

3. If God did not exist, the world would be better.4. If God did not exist, the world would be worse.

Both 3 and 4 are false on Davis and Franks’s account because the consequent implies the existence of at least one thing (namely, the world),8 but according to the null world hypothesis if God did not exist, neither would the world.9 Thus, 3 and 4 both meet Davis and Franks’s sufficient condition for falsehood. Although we can assign non-arbitrary truth-values to 3 and 4, surely we need one to be true and the other false if we are to avoid agnosticism or quietism about 7 Kahane (2011) suggests that counterpossibles might be intelligible, but does not say how. He then drops this suggestion in his 2012 paper.8 I am assuming that the world’s having value implies the existence of the world.9 Mark Murphy suggests that I may be equivocating on the term ‘world’ in applying Davis and Franks’s account. In one sense, ‘world’ denotes a contingently existing thing (‘the world would not exist’). In another sense, ‘world’ means ‘everything that is the case.’ Arguably, the null world hypothesis concerns ‘world’ in the first sense, but 3 and 4 concern ‘world’ in the second. I have two responses. First, while one could read 3 and 4 in the second sense, it is not compulsory: ‘world’ in 3 and 4 may denote the world as an object. Second, while the null world hypothesis does concern the world as an object, it concerns something stronger: without God nothing would exist. So nothing would be the case. Thus, the null world hypothesis should be read as concerning the ‘world’ both as an object and as ‘everything that is the case.’

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the axiological question. Thus, although Davis and Franks have provided a non-standard semantics, their semantics fails to avoid quietism about the axiological question.10

Similarly, Kahane (2012) claims it is not a “useful solution…to our problem” for the theist to claim that “if we can even conceive of [a world without God], what we must conceive is an empty void, containing no value” (p. 38). I agree with Kahane that the theist’s retreat to the null world hypothesis does little to aid in answering the axiological question. If we follow Davis and Franks’s semantics, and God exists necessarily (as they think), then all claims about what the world would be like if God did not exist are false.

Even some theists might resist this null world retreat. Again, consider pragmatic reasoning about God’s existence. Pascal’s counterpossible reasoning about whether he ought to believe that God exists includes causal reasoning about what belief that God exists (and belief that God does not exist) would entail in a godless world. The null world retreat threatens more than just the axiological question: it threatens any pragmatic reasoning about belief/acceptance of God’s existence. One might object here that Pascal’s Wager, and pragmatic arguments for the rationality of belief that God exists generally, are aimed at the agnostic, not the necessitarian theist or atheist. However, the necessitarian theist and necessitarian atheist can still trace through the argument. On the theist’s null world retreat, the following are both false:

7. If God does not exist, then S stands to lose nothing by believing that God exists.8. If God does not exist, then S stands to gain nothing (or very little) by not believing that

God exists.

Thus, even some theists might resist the null world retreat—especially those sympathetic to practical arguments for God’s existence.

3. Cognitive decoupling in imagination and pretense

We need a new response to the quietist. I argue that we may find a solution by examining the nature of human counterfactual reasoning and pretense combined with a three-valued logic. Developmental psychologist Allan Leslie (1987) asks “how is it possible for a child to think about a banana as if it were a telephone, a lump of plastic as if it were alive, or an empty dish as if it contained soap?” (p. 412). Children can represent an object as what it is while simultaneously representing it as having incompatible properties. Furthermore, this does not lead to any contradictions in their thinking. How is this possible? Leslie posits the existence of a ‘decoupling mechanism.’ On his account, children representing a banana as a phone possess a primary representation of the world and a copy of the primary representation, which is “in effect not [a] representation of the world but [a] representation of [a] representation” (p. 417). Children use the metarepresentation to engage in pretend play. It is because the metarepresentation is not generated by the world, but is generated from a representation of the world, that children are able to treat it as pretend and avoid becoming confused as to what is real. He also points out that the existence and use of the metarepresentation leaves the primary representation intact, and so the primary representation “is free to continue exerting whatever influence it would have on ongoing processes” (p. 417). This is why a child wielding a whiffle-ball-bat as a sword can represent the

10 This is not to say that Davis and Franks’s defense of divine command theory is ill conceived or problematic. My claim is merely that the strategy will not avoid the charge of quietism about the axiological question. If Davis and Franks are right in defending divine command theory from the terrible deity objection by way of reconceiving of counterpossibles, it should be done using the three-valued logic I propose below.

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bat as a sword, but simultaneously recognize that swinging it into a friend will not actually cut them. The child must suppress the primary representation of the bat, which includes that the bat is yellow, made of plastic, etc.

Nichols and Stich (2003) improve on Leslie’s account and argue that we need a new kind of mental state called ‘supposing’ in order to account for pretense, which cannot be reduced to belief and desire. ‘Supposing’ is similar to a number of other proposed belief-like states such as ‘hypothesis,’ ‘premise,’ ‘acceptance,’ and ‘imagining’ (Alston, 1996, 2007; Bratman, 1992; Cohen, 1992; Engel, 2012; Frankish, 2004; Stalnaker, 1984). For my purposes here, I will talk in terms of ‘supposing,’ but any mental ontology distinguishing belief from some other belief-like state should be amenable to my suggested approach of counterpossibles. Thus, in addition to there being a ‘belief box’ and ‘desire box’ in their computational account of reasoning, there is a ‘possible world’ box.

The possible world box only indirectly affects beliefs because all interactions between beliefs and suppositions are mediated through inference formation. One important inference mechanism is called ‘updater,’ which searches for inconsistencies and alters beliefs as circumstances change or novel beliefs are acquired. Most importantly for my purposes, updater ‘screens out’ beliefs that are inconsistent with those propositions currently in the possible world box. There are three crucial claims on Nichols and Stich’s account. First, the very same inference mechanism operates on suppositions and beliefs (p. 29). Second, suppositions and beliefs do not differ in the type of content (the two are of the “same logical form” p. 32). Third, suppositions and beliefs may combine in inferences (p. 32). Because Nichols and Stich’s aim is to defend their own account of hybrid folk psychology (combining theory-theory and simulation-theory), they spend little time considering the important implications for counterfactual reasoning.

Stanovich (2011) applies Leslie’s and Nichols and Stich’s accounts to counterfactual reasoning (or what he calls ‘reflective thinking’). Stanovich (2011) claims that when we engage in novel counterfactual reasoning, subjects can represent a possible world in which the premises are true, and then search for a counter-example to the conclusion. While Stanovich’s account is theory-laden within a problematic dual-process framework (see Osman 2004; Keren and Schul 2009; Kruglanski & Gigerenzer, 2011; and Mugg 2013, Mugg 2015 a, and Mugg 2015 b), he is right in emphasizing the importance of cognitive decoupling in human reasoning.

4. Pretending that God exists (or does not exist)

Cognitive decoupling occurs when subjects extract information from a representation and perform computations on that extracted information. What is crucial to cognitive decoupling is the ‘screening out’ of information. I will say that beliefs are ‘screened out’ just in case they are kept separate from the reasoning process (i.e. they do not figure as premises in the argument and exert no causal influence over the reasoning process). Those beliefs that are allowed into the reasoning process, along with the suppositions, are ‘cognitively quarantined’ from the subject’s beliefs. Consider the following syllogism:

9. All whales are mammals.10. All whales nurse their young.

Therefore,11. All mammals nurse their young.

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I am sure you recognized that this syllogism is invalid, even though 9-11 are all true. How did you do so? One way is to construct an imagined state of affairs in which the premises are true and check whether the conclusion must be true in that state of affairs. In doing so, you must ‘screen out’ the belief that 11 is true. That is, you must ignore that 11 is true and keep the truth of 11 from interfering with the reasoning process whereby you judge whether 11 follows from 9 and 10.11 A plausible explanation of some instances of belief bias (the effect of the believed truth-value of a conclusion on the judged validity of an argument) is that some subjects fail to screen out some of their beliefs (see Evans, Barston, and Pollard 1983).

Consider counterfactual reasoning. When considering what it would be like if I were a professional truck-driver, I must screen out my belief that I am a philosopher living in Kokomo, Indiana. Now, when considering a counterfactual, subjects can screen out those beliefs that (with the antecedent of the counterfactual) imply contradictions. To use Nichols and Stich’s account, I suppose that I am a truck-driver, and then only allow this supposition to interact with those beliefs that do not imply contradictions.

Now consider counterpossible reasoning. Notice that many conceptual truths are loosened in certain genres of fiction. For example, Bugs Bunny might pick up a hole off the ground and throw it on a wall. It is not metaphysically possible to pick up a hole, but we are able to suppose that Bugs has picked up the hole and recognize that Bugs can now jump through the wall. Thus, we can imagine an impossible state of affairs and make judgments about what would obtain within that state of affairs. In representing the impossible state of affairs, we screen out those beliefs that would lead to outright contradiction. In Bugs’s hole case, we must screen out certain beliefs regarding the nature of holes (i.e. that they cannot be picked up).

Counterpossible reasoning does not just occur within fanciful fiction. Similarly, philosophers engage in counterpossible reasoning. Suppose an endurantist who believes perdurantism to be necessarily false receives an undergraduate paper outlining how perdurantism fits with certain views of material constitution. How will the professor proceed? Hopefully this professor will do so by assuming that perdurantism is true and then seeing if the student’s solutions to problems surrounding material constitution are successful on that assumption. Thus, the endurantist philosopher engages in (what that professor takes to be) counterpossible reasoning.12 I suggest that the professor is able to do so by supposing that perdurantism is true and then screening out those beliefs that would render perdurantism necessarily false (e.g. that presentism is necessarily true).

On this account of cognitive architecture, in order to consider an impossible state of affairs, subjects form a single ‘supposition’ and then screen out certain beliefs from that supposition. Some subset of the remaining beliefs, combined with the suppositions, are then cognitively quarantined. Subjects use these cognitively quarantined beliefs and suppositions in inferences resulting in further suppositions. My suggestion is that the representation of the state of affairs is constituted by the cognitively quarantined beliefs and suppositions.

Counterfactual states of affairs can be maximal: for any proposition in a counterfactual state of affairs, that proposition is either true or false. Indeed, when we reason about a counterfactual state of affairs, it is best to do so in as maximal a way as we can. This is not the

11 There are other ways to assess validity, such as attending only to syntactical form, or making Venn Diagrams. Although we can assess validity in these alternative ways, it seems we often do reason about validity by way of accepting the premises and checking if the conclusion necessarily follows. 12 If you do not like this example, I invite you to consider how you proceeded to review any paper where you thought that some assumed (for the purposes of the paper) proposition is necessarily false. I suspect that you were able to suppose that the assumption was true and proceed accordingly.

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case when we represent impossible states of affairs. The representation of the impossible state of affairs must be partial because some propositions (along with the denial of those propositions) must be screened out. Those beliefs that are screened out are not false, but disregarded or ignored.13

Figure 1: ‘Waterfall’ by Escher

Perhaps an example will help. Consider a picture of an impossible object, such as ‘Waterfall’ by Escher. The object that this picture represents could not exist, but this is no problem for our representing it. Thinking about the properties of the impossible object only becomes problematic when we try to conceive of what is represented in the picture as a whole. If we cover parts of the aqueducts in ‘Waterfall,’ we are able to make sense of the (partial) object. The result is that, in considering counterpossibles, we should not attempt to conceive of maximal states of affairs (i.e. states of affairs in which every proposition is either true or false). Instead,

13 Importantly, my claim is not that impossible states of affairs themselves are only partial. I am not making a claim about the nature of impossible states of affairs as such. My claim is that the representation of impossible states of affairs are partial.

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some propositions must be left out altogether. Thus, when we evaluate what would be the case in an impossible state of affairs, we should conceive of partial impossible states of affairs.

5. Distinguish 1-4: A Non-Standard Semantics

In order to meet the quietist objection, we need a way of reasoning about impossible states of affairs and a way to give non-trivial truth-values to counterpossible conditionals. Thus far I have only offered the former. My account of the possibility of counterpossible reasoning relies on our ability to cognitively quarantine propositions by screening out, or ignoring, some propositions. Thus, I suggest that when we reason about impossibilities, we are not using a standard, two-valued logic: we are using a many-valued logic. Here I will use Kleene’s Strong System to show the basic idea. In this system there are three values: True (T), False (F), and Neither True nor False (N). Usually Kleene’s N is used as ‘indeterminate,’ often relative to some current body of evidence. Given my previous discussion, we should think of ‘Neither True nor False,’ in the present discussion, as ‘Screened Out.’ The truth-tables for the logical connectives in Kleene’s Strong System resemble that of classical logic, which is why I chose this three-valued logical system. Since conditionals are our most pressing concern here, I will only include its truth table:

ConsequentT N F

Ant

eced

ent T T N F

N T N NF T T T

A nice feature of Kleene’s Strong System is that we may use a standard truth-preserving definition of validity, and we may keep all the standard inference rules. Of course, the above truth-table is for material conditionals, but here we are concerned with counterpossible conditionals. We may reinterpret the standard possible world semantics using Kleene’s Strong System. For counterfactuals, we look at the closest possible world in which the antecedent is true, and determine if, in that world, the consequent is true. For counterfactuals, only the top row (true antecedent) is relevant.

Counterpossibles require slightly more revision. We must divide counterpossibles into two categories. If the antecedent of the counterpossible is one that we can, at least to some degree, contemplate, then we may treat it in a similar manner as a counterfactual.14 However, we do not go to the closest possible world in which the antecedent is true, since there is no such world. Instead, we move to the closest (partial) state of affairs. Some propositions in that state of affairs are screened out—given the value N. The counterpossibles concerning Bugs and perdurantism are like this.

When I consider Bugs picking up a hole, I imagine a (partial) state of affairs in which Bugs picks up a hole. That is, I pretend that holes can be picked up. In doing so, I screen out much of what I know about holes (e.g. that they cannot be picked up). I then consider what would happen, in that (partial) state of affairs when Bugs jumps through the the hole that is now on the wall. In doing so, I recognize that Bugs would be able to pass through the hole on the wall, but not through other points on the wall. Thus, the counterpossible ‘if Bugs attempts to 14 Zagzebski (1990) similarly distinguishes between counterpossibles whose antecedents are contradictions, and those whose antecedents are ‘interesting impossible propositions.’

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jump through the hole he has thrown on the wall, he will pass through the other side’ is true, while the counterpossible ‘if Bugs attempts to jump through the wall two feet to the left of the hole on the wall, he will pass through to the other side’ is false. In each case, the antecedent is true in the (partial) state of affairs I am imagining. However, in the first counterpossible, the consequent is true, while in the second, the consequent false.

Now, there are some counterpossibles in which the contradiction within the antecedent is too glaring for us to move to a partial state of affairs in which the antecedent is true. Consider Quine’s example of a round square copula on Berkeley College. In order to move to a partial state of affairs in which this antecedent is true, I would have to screen out part of the antecedent itself (either ‘round’ or ‘square,’ on the one hand, and ‘copula’ or ‘being on,’ since copulas are not located, on the other). Thus, I must move to a (partial) state of affairs in which the antecedent is N, screened out, rather than true. Thus, when dealing with a counterpossible in which the contradiction is expressed in the antecedent itself, we use the second row of the above truth-table. Thus, these counterpossibles will never be false. They can only be true or N, screened out.15

It seems that a three-valued logic nicely models the above account of pretense.16 The propositions that we treat as N (screened-out) are those propositions that we totally ignore. In actual cases of pretend play, we ignore certain propositions so naturally that it does not seem worth mentioning which propositions we screen out. For example, children screen out the proposition ‘something cannot simultaneously be composed entirely of yellow plastic and steel’ when wielding a whiffle-ball-bat as a sword. Notice that it is not that the child treats the above proposition as false. Rather, the child ignores it altogether. Or consider the following from Gould (1972): a 3‐year‐old boy on a jungle gym said, “ ‘I'm a pussycat. Meow, meow.’ He then came down from the jungle gym and lay on the ground, saying, ‘I'm dead. I'm a dead pussycat . . . I got shooted’ ” (Gould 1972: 212, quoted in Nichols and Stich 2003: 20). The boy treats some false propositions as true (e.g. ‘dead things cannot talk,’ ‘cats cannot talk’). However, he also screens out some propositions. We begin to see them as we try to work through how it would be that this dead cat is talking. Dead things are not breathing, yet vocal speech requires air in the lungs. Now, it could be that the boy is treating the proposition ‘vocal speech requires air in the lungs’ as false, but not necessarily so. Plausibly, he is simply not considering the proposition at all, which is to say that it is screened out.

Let us return to the counterpossibles at issue when we attempt to address the axiological question of God’s existence:

1. If God were to exist, the world would be better.2. If God were to exist, the world would be worse.3. If God were not to exist, the world would be better.4. If God were not to exist, the world would be worse.

When subjects assess 1-4, they must screen out those beliefs that generate contradictions when combined in inference formation with one of the antecedents of 1-4. That is, we assign

15 One might object here that the treatment of this second set of counterpossibles implies quietism. I will return to this in the objections section below.16 Exactly what children are doing in pretense is an empirical question. My solution to the quietist challenge does not depend on the empirical question of what children are actually doing. My purpose in using a three-valued logic for pretense is simply to show that pretense can be modeled this way, and so, application of a three-valued logic combined with the above account of pretense is perfectly coherent.

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those propositions that generate contradictions the truth-value ‘N.’ Crucially, we must not screen out the proposition ‘God exists’ when considering godly worlds, and we must not screen out the proposition ‘God does not exist’ when considering godless worlds. To see why, consider a theist who screens out the proposition ‘God does not exist’ in a godless world. To avoid quietism, either 3 or 4 should turn out to be true, and the other false. However, if ‘God does not exist’ is screened out, it has truth-value N. In that case, the antecedent of 3 and 4 will be N. Looking back at our truth-table, note that the conditional can only be false when the antecedent is true and the consequent false, as in classical logic. A theistic pro-theist could affirm the truth of 4 but not the falsity of 3, and the theist anti-theist could affirm the truth of 3 but not the falsity of 4. This same problem can be extended to atheism. Thus, we should not screen out the proposition ‘God exists’ in considering godly worlds or ‘God does not exist’ in considering godless worlds. Instead, what we screen out is the proposition ‘God exists is a necessary proposition’ or ‘God does not exist is a necessary proposition.’

Some conceptual truths, on which the atheist, agnostic, and theist might all agree, must be screened out. For example, the claim that ‘if God were to exist, God would exist necessarily’ must be screened out. Furthermore, for any set of propositions that entail this proposition, some subset of those propositions must be screened out. Of course, the beliefs that must be screened out differ for the theist and atheist. The theist must screen out beliefs ‘God exists necessarily,’ ‘if God did not exist, neither would anything else,’ and so forth. Similarly, the atheist must screen out beliefs such as ‘the very idea of God is incoherent,’ ‘God’s existence is logically incompatible with the existence of evil,’ and so forth.

In practice, it seems that philosophers working on the axiological question have tended to conceive of impossible states of affairs in partial ways and emphasize which propositions are maintained as true within the godly or godless states of affairs. To clarify my approach, I will outline Kahane’s (2011) argument using this new method. Again, my purpose is not to defend pro-theism or anti-theism, but rather to show how my method can be applied in practice. My method can be extended to other arguments for and against pro-theism and anti-theism (see Penner and Lougheed 2015, Penner 2015, McLean 2015, Dumsday forthcoming, Kraay and Dragos 2013).

Kahane’s argument for anti-theism proceeds in two steps. In step one, Kahane argues that the world would be worse in certain respects if God did exist. Second, Kahane admits that the world might be better overall in certain other respect, but that these respects do not outweigh the values lost by God’s existence from the perspective of the individual. Thus, Kahane is a personal anti-theist rather than an impersonal anti-theist. I will apply my approach only to Kahane’s argument concerning impersonal pro-theism/anti-theism.17 In support of the first step, speculating on Nagel’s claim that he “hopes the world is not like that,” Kahane writes:

A world in which God exists is a world where human beings stand in a distinctive and inescapable relation to another person. It is a world where we are the subordinates of a moral superior…and where we have been created to play a part in some divine cosmic plan. It is a world where everything about us is known and fully understood by another, a world where even our innermost thoughts and feelings are not entirely private. It is a world in which we are never truly alone, away from the presence and attention of another. And if the true nature of God is beyond human comprehension, it would also be a world that we can never hope to fully understand. The idea is that God’s existence is logically incompatible with the full realization of certain values. Thus a world in which God exists is a world where we would not be the moral equals of all other rational beings—equal members of a kingdom of ends that has no ruler. Such a world seems incompatible

17 Applying my approach to Kahane’s views on personal anti-theism is just more-of-the-same.

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with complete independence, or with complete privacy and genuine solitude. And it might also be a world where it would be pointless for us to strive for a complete and unqualified understanding of the universe. (Kahane 2011, 681-682)

Kahane admits that this is not yet an argument because he has not offered a full account of “values such as independence and privacy” nor “demonstrate[d] that, on some common understanding of the concept of God, their full realization is incompatible with God’s existence” (684). However, we can at least see how my method for analyzing counterpossibles helps us make sense of the above reasoning. Pretend that God exists (I write here as though I am a necessitarian atheist). We imagine a (partial) state of affairs in which there is a being (call him ‘God’) which is supremely powerful, knowing, and good. I screen out the proposition ‘if God exists, he exists necessarily.’ This being would know everything about me. Thus, if God existed, I would not have privacy, since something is private only if only one person knows it. The antecedent is true in the (partial) state of affairs, and so is the consequent. Thus, this counterpossible is true. Presumable privacy is valuable, and so we lose one thing that is valuable in the Godly world. Similar reasoning applies to the other values outlined above (equality, independence, and understanding).

However, Kahane admits that “it is very likely that a world in which God exists is significantly better overall” (2011, p. 687). This is because in that Godly world, there would be some solution to the problem of suffering. As he puts it:

“The suffering of the innocent must somehow be compatible with God’s goodness—perhaps such evil is compensated by some far greater good. But if something like this solution to the problem of evil is successful, why shouldn’t it also be possible for God to provide enough good to outweigh the badness of our being deprived of goods like full independence or privacy? Surely the impossibility of complete independence could not matter more than the suffering of the innocent?” (2011, p. 686).

The key proposition in the problem of suffering is this: ‘if God exists, then evil does not.’ Kahane suggests that this proposition is false in the Godly (partial) state of affairs. If God did exist, then there must be some reason for which God allows suffering. However, if, as some atheists have claimed, God’s existence is logically incompatible with the existence of evil, then the conditional in question is not false, but screened out in that (partial) state of affairs. Thus, it is not necessarily the case that, in that (partial) state of affairs, God has a reason for allowing evil. The counterpossible ‘if God existed and suffering existed, then God would have a reason for allowing suffering’ would be N, since it would have a true antecedent and an N consequent, rendering the overall statement N, screened out.

Of course, many atheists do not claim that suffering is logically incompatible with God’s existence, just that it renders God’s existence unlikely. In that case, there is no need to screen out the proposition ‘if God exists, then God has a reason for allowing suffering.’ Thus, for one endorsing only the evidential argument from suffering, Kahane is right that if God existed and suffering existed, then God would have a reason for allowing suffering. Kahane goes on to claim that God ensuring some morally satisfactory reason for allowing suffering would outweigh the goods lost (privacy, understanding, equality, independence). Thus, overall (or impersonal) pro-theism is true, though for a great number of individuals, the goods lost are more important than the goods gained, and so personal anti-theism is true for those individuals.

6. Objections and replies

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Pro-theists might become worried here. Surely God’s perfection and goodness (if God were to exist) will figure prominently in their arguments for pro-theism. But, it is often maintained, one implication of perfection is existence. Thus, pro-theists cannot use God’s perfection in an argument for pro-theism. The deck has been stacked against them. However, this would be too hasty, since there are two claims in this short argument: first, that God (if such there be) is perfect, and second, that perfection implies existence. We must keep one of these claims out of the present debate, and perhaps it is better to screen out the second, rather than the first. On this suggestion, the claim that ‘perfection implies existence’ is N (screened out) in the (partial) state of affairs. However, the claim ‘God is perfect’ would be true in the (partial) state of affairs. Thus, pro-theists may use God’s perfection in their arguments.

One might object that my account looks remarkably similar to Kahane’s, which I rejected. Recall Kahane’s preferred strategy: the atheist who maintains that the existence of an omniscient, omnibenevolent, omnipotent being is incoherent should consider a possible world in which there is a very knowledgeable, very benevolent, very powerful being. His suggestion is to water down the theist’s claims. This is not what I propose. Rather, I suggest that some subset of the propositions leading to the claim that God’s existence is incoherent be screened out. To use my Escher analogy, my suggestion is to cover up part of the aqueduct, while Kahane’s is to consider a different aqueduct altogether.

Some philosophers of religion might object to my approach on grounds that they cannot conceive of God failing to exist: it is a psychological impossibility. Similarly, some philosophers and theologians will claim that they simply cannot screen out certain propositions that entail God’s existence. Some might make the stronger claim that when a subject’s cognitive faculties are properly functioning, that subject must believe that God exists. Since these philosophers cannot screen out the appropriate beliefs, the objection concludes, my account does not allow these philosophers to engage in the axiological question

For the sake of argument, assume that the objector is right in thinking that a properly functioning cognitive system produces belief that God exists. Notice that my account does not require that the theist disbelieve that God exists, or that the atheist believe that God exists, when considering what they take to be counterpossibles. Nor does it require that either suspend judgment on the existential question of God’s existence. All my solution requires is that theists screen out their belief that God exists when they consider Godless worlds and that atheists screen out their belief that God does not exist when they consider Godly worlds. The belief, though screened out, is “free to continue exerting whatever influence it would have on ongoing processes” (Leslie 1987, p. 417).

I admit that my approach will be of no help to theists who deny that they can even imagine God not existing, or atheists who claim that they cannot imagine God existing. If a theist claims not only that godless states of affairs are impossible, but that it is impossible to even imagine them, then this theist is committed to quietism, assuming that the axiological question is comparative. The axiological question will require comparing the value of godly and godless states of affairs, and this requires at least imagination. These theists might be able to speak of the effect God has on this world, but they will be unable to compare those goods or ills to any other world.

Admittedly, some impossibilities are such that I cannot conceive of them, and quietism about them may be fitting. I cannot imagine of a round square copula on Berkeley College, but I am not troubled by this. First, remember that counterpossibles with ‘there is a round square copula on Berkeley College’ as an antecedent need not always be true. On my account, they can

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be N, screened out, and this happens if the consequent is N in the closest possible state of affairs. Thus, counterpossibles like: ‘if there is a round square copula on Berkeley College, then dolphins are not dolphins’ is not true nor false. Rather, it is N, screened out. Perhaps, this is a form of quietism (after all, these kinds of counterpossibles cannot be false, only true or N). However, and this is the second point, even if this is a kind of quietism, quietism about those counterpossibles might be just fine. Quietism about the value that a round square copula on Berekeley College might be justified. However, I don’t think that ‘God exists’ or ‘God does not exist’ are on a par with ‘there is a round square copula on Berekeley College.’ The counterpossibles involving God’s existence (or non-existence) are on a par with Bugs picking up holes, and these counterpossibles can be false. Most of us can at least imagine godly and godless states of affairs, and that puts the counterpossibles in question (1 and 2, or 3 and 4) in the first category of counterpossibles.

7. Conclusion

I have offered an account of the possibility of reasoning about the impossibilities. Beliefs toward certain propositions must be screened out from the cognitive processes by which we evaluate the goodness of God’s existence. I have applied Nichols and Stich’s (2003) model of pretense to counterpossibles in order to offer a non-standard semantics, but my strategy does not turn on the details of their account. Any philosopher adopting a distinction between belief (on the one hand) and acceptance, hypothesis, supposing, or premising (on the other) may avail themselves of my account. This model can be extended to other arguments involving counterpossibles.18 The upshot for the axiological question is that, if philosophers wish to avoid quietism, they must ignore certain beliefs about God’s nature. Admittedly, I have not actually said which of 1-4 are true and which are false. However, doing so would be to answer the axiological question, and my purpose in this paper was only to say how we could make sense of the question.19

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18 See Zagzebski (1990, p. 179-180) for four examples.19 I presented an early version of this paper at the Toronto Philosophy of Religion Work in Progress Group. Many thanks to Paul Franks, Rich Davis, Jennifer Hart Weed, and Klaas Kraay (who also provided comments on a written draft. I also presented this paper at the 2015 Eastern Meeting of the Society for Christian Philosophers. Thank you to audience members. This paper benefited from comments from Mark Murphy and three anonymous reviewers.

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